We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement —order-from-disorder— is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.
We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement —order-from-disorder— is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.
We investigate equilibrium statistical properties of the isotropic quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or annealed disorder or both. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales---the time scale associated with the equilibration of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We find that the magnetization survives in the presence of a unidirectional random field, irrespective of its nature, i.e., whether it is quenched or annealed. However, the field breaks the circular symmetry of the magnetization, and the system magnetizes in specific directions, parallel or transverse to the applied magnetic field. Interestingly, while the transverse magnetization is affected by the annealed disordered field, the parallel one remains unfazed by the same. Moreover, the annealed disorder present in the interaction term does not affect the system's spontaneous magnetization and the corresponding critical temperature, irrespective of the presence or absence of quenched or annealed disorder in the field term. We carry out a comparative study of these and all other different combinations of the disorders in the interaction and field terms, and point out their generic features.
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of fourfold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one-dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one-dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.
We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins--for classical and quantum correlations--is related to the quantum critical point in the corresponding ordered system.
We investigate the behaviour of quantum correlations (entanglement and
quantum discord) for homogeneous XY model at absolute zero and at finite temperature. Study of this correlation measures of quenched disordered
quantum spin models like the XY spin glass and random-field XY models is
also reviewed. We show that quenched averaged quantum correlations can
showcase the order-from-disorder phenomenon for finite-size systems and also
when the system is in the thermodynamic limit. Though we find some regions
with positive enhancement score. This order from disorder phenomena
is more prominent when the system is in the finite temparature with some
definite values of external parameter. We also look into correlation length.
Correlation functions of ground states typically decay exponentially with the
distance for quantum spin systems. In such systems, entanglement does not
survive when |i-j| ≳ 3. However, quantum discord survives long lattice
distances as it is not monogamous for this system. We investigate the effects
of quenched disorder on quantum correlation lengths of quenched averaged
entanglement and quantum discord, in the anisotropic XY spin glass chains.
We realize that there is practically neither diminution nor growth in entanglement
length while quantum discord length increases significantly with
the introduction of quenched disorder except near factorization point. Apart
from that, we also investigate the scaling behaviour of quantum entanglement
and quantum discord. We find that though entanglement follows finite size
scaling close to quantum phase transition, scaling can't be done for quantum
discord.
The time dynamics of quantum correlations in the quantum transverse anisotropic XY spin chain of infinite length is studied at zero and finite temperatures. The evolution occurs due to the instantaneous quenching of the coupling constant between the nearest-neighbor spins of the model, which is performed either within the same phase or across the quantum phase-transition point connecting the order-disorder phases of the model. We characterize the time-evolved quantum correlations, viz., entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the quenching scheme. We show that the system is endowed with enhanced nearest-neighbor bipartite quantum correlations compared to that of the initial state, when quenched from the ordered to the deep disordered phase. However, nearest-neighbor quantum correlations are almost washed out when the system is quenched from the disordered to the ordered phase with the initial state being at the zero temperature. We also identify the condition for the occurrence of enhanced bipartite correlations when the system is quenched within the same phase. Moreover, we investigate the bipartite quantum correlations when the initial state is a thermal equilibrium state with finite temperature, which reveals the effects of thermal fluctuation on the phenomena observed at zero temperature. Finally, an analogous analysis is carried out for zero-temperature next-nearest-neighbor quantum correlations.
Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of a one-dimensional array of quantum spin-1/2 particles, governed by the Heisenberg spin glass Hamiltonian with natural or engineered quenched disordered couplings in an external magnetic field. These systems allow disorder-induced enhancement for bipartite and multipartite observables. Here we show that simultaneous application of independent quenched disorders results in disorder-induced enhancement, while the same is absent with individual application of the same disorders. We term the phenomenon as constructive interference and the corresponding parameter stretches as the Venus regions. Interestingly, it has only been observed for multiparty entanglement and is absent for the single- and two-party physical quantities. Introduction and background Disordered systems form one of the center-stages of research in many body sciences and lead to a plethora of interesting phenomena and applications. Presence of disorder may lead to nontrivial and counterintuitive properties as compared to their homogeneous counterparts. Prominent examples are novel quantum phases, localization, high-Tc superconductivity and disorder-induced ordering. In this work, we consider paradigmatic disordered systems consisting of a one-dimensional array of quantum spin-1/2 particles, governed by quenched disordered quantum Heisenberg Hamiltonians in external magnetic fields. The primary goal of this work is to understand the bi- and multi-partite quantum entanglement due the interplay of planer and azimuthal couplings when disorder is present in either one of them or both of them. Main results We have examined the behavior of magnetization, two-party classical as well as quantum correlations, and multipartite entanglement for the ground states of quenched disordered quantum Heisenberg spin systems for sizes ranging from five to twenty quantum spin-1/2 particles. The quenched disorder is present in the planar, or the azimuthal couplings, or in both. Our main results are the following. Firstly, in presence of the impurities in the couplings, there exist different parameter regions for different physical quantities, which show disorder-induced enhancement. We identify the parameter stretches where the phenomenon of disorder-induced enhancement corresponding to the quantities under investigation occurs for different possible cases, viz., when disorder is present in either of the interaction terms or disorder is present in both the interaction terms. Secondly, we ask a rather radical question: Is it possible to have disorder-induced enhancement of a physical quantity by the insertion of two types of disorder in a single system, while the disorders when present in the individual interaction terms do not provide any increment? We answer the question in the affirmative provided the external field strength is greater than a cut-off value. We term the phenomenon as "constructive interference" and the corresponding parameter stretches as the "Venus" regions. Interestingly, it has only been observed for multiparty entanglement and is absent for the single- and two-party physical quantities. Wider implications Firstly, the seemingly counterintuitive nature of constructive interference for a physical quantity leads us to believe that it can have implications in fundamental and application regimes. Moreover, multiparty quantum information processing tasks typically have origins in the bipartite domain. Instances where the converse occurs are few and far between, and indicate important diversions from the usual track. Secondly, a detailed knowledge on the effect of disorder on quantum correlations is highly desirable in order to assume perfect control over quantum technologies based on quantum spin magnetic systems. Thirdly, it is interesting to think about possible connections of disorder-induced enhancement with other interesting quantum phenomena such as many-body localization.